...as nearly as I can tell, there’s almost nothing to be learned about it on the English-speaking internet. It appears to be either a remake or a hack of a German game that was known as both Bobby Geht Heim and Bobby Geht Nach Hause, which was also remade or hacked as Jumping Jack. My only reason for thinking Lilly Adventure is a later version is that it is, for the most part, better looking.
Whatever the history of Lilly Adventure, it can hardly be as convoluted as the game itself. The gameplay concept–walk from left to right and jump over both static and moving objects, was not new, but Lilly Adventure puts a crazy twist on it. The enemies you encounter look like the savages from Jungle Hunt and the amorphous blobs from Activision’s unreleased puzzle game Kabobber -- not what you'd expect to find on a journey through what looks like the European countryside. What’s particularly odd is that while the game’s background art, and Lilly herself, both look good for their time, everything else looks rather crude.